Weyl’s theorem and Putnam’s inequality for class \(p-wA(s,t)\) operators. (English) Zbl 1424.47051
Let \(T\) be a bounded linear Hilbert space operator and let \(\vert T\vert =(T^\ast T)^{1/2}\) . Let also \(0<p<1\) and \(s,t>0\). The operator \(T\) is said to be class \(p - wA (s,t)\) if
\[
(\vert T^\ast\vert ^t \vert T\vert ^{2s} \vert T^\ast\vert ^t)^{\frac{tp}{s+t}}\geq \vert T^\ast\vert ^{2tp}
\]
and
\[
(\vert T\vert ^2 \vert T^\ast\vert ^{2s} \vert T\vert ^s)^{\frac{tp}{s+t}}\leq \vert T\vert ^{2sp}.
\]
This extends the concept of \(p\)-hyponormal and log-hyponormal operators. Class \(p - wA (s,t)\) operators have been studied extensively in several recent papers, see, for example, M. Chō et al. [Acta Sci. Math. 82, No. 3–4, 641–649 (2016; Zbl 1399.47077)]. The present paper continues this study. The authors provide a number of useful results about this class of operators. Among other things, they prove a Weyl-type theorem and a Putnam-type inequality.
Reviewer: Khristo N. Boyadzhiev (Ada)
Citations:
Zbl 1399.47077References:
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